Data Handling and Statistical Analysis

Data Handling and Statistical Analysis

The Biology Department has enhanced its laboratory courses with exercises in data handling and statistical analysis. The department encourages students to use SPSS for the display and analysis of data generated in laboratory courses and in research. The Student User Guide for SPSS introduces students to the program’s capabilities in several courses.

Laboratory in Ecology

Population Growth in Lemna

In this experiment, students establish cultures of floating aquatic plants and then monitor their population growth. At the end of the experiment, they use nonlinear regression analysis to determine whether the cultures followed the predictions of exponential and logistic population growth models.

At Barnard, we grow Lemna (available from biological supply houses and tropical fish stores) in 120 ml of half-strength Murashige and Skoog Modified Basal Salt Mixture (available from Phytotechnology Laboratories, Product No M571) prepared with bottled spring water. The cultures are maintained at room temperature in small plastic containers placed about 5 cm below grow-light fluorescent bulbs. After setting up their cultures students count the thalli (>1.5 mm) every Monday, Wednesday, and Friday. Containers are refilled with spring water to compensate for evaporation before each count. The growth medium is changed and the cultures are cleaned of algae weekly.

Students plot population size versus time for each culture on a daily basis. When the population has filled the container - or when population size has leveled off - students use nonlinear regression to evaluate their data against exponential and logistic models of population growth. The analysis is outlined in the accompanying files: one describes the analysis in SPSS and the other provides an Excel template for graphing both the data and the calculated nonlinear regressions.

To save time, we have usually encouraged students to start some cultures with 2 thalli (representing the early stages of population growth) and other cultures with 15 thalli (representing later stages of population growth). They combine the two data sets when the cultures started with 2 thalli reach a population size of 15. In the future, we will probably simply start all cultures with 5 thalli and then follow them until population growth has filled the containers. The analysis described in the accompanying files is based on the 2 thalli/15 thalli procedure, but it can be easily adapted to any initial population size.

Competition in Paramecium

In this experiment, students evaluate interspecific competition between two species of Paramecium by growing each species alone and in combination with the other. They monitor population growth under both conditions and then use nonlinear regression analysis to estimate parameters for the logistic population growth model and the competition coefficients.

At Barnard, we grow Paramecium (available from biological supply houses) in 40 ml centrifuge tubes. The culture medium is made from protozoan pellets (ground hay) and boiled wheat seeds (both available from Carolina Biological). Culture and sampling methods are detailed in Experiments to Teach Ecology, a 1991 publication of the Ecological Society of America (see third exercise at http://tiee.ecoed.net/vol/expv1/expv1_toc.html#3).

We have had the greatest success with the following Paramecium species: P. aurelia, P. bursaria, P. caudatum, and P. multimicronucleatum. Because the vitality of the cultures varies considerably from year to year, it is helpful to maintain stock cultures of all four species. Any combination of species may be used, but pairing P. aurelia with either P. caudatum or P. multimicronucleatum is appropriate because the former species is much smaller than - and easy to distinguish from - the other two. P. bursaria also makes a good match to any of the other species because it contains a markedly green photosynthetic endosymbiont. Students can also design experiments involving the effect of light intensity on population growth of P. bursaria.

Cultures are maintained on a 12:12 L:D light cycle at 21°C. Students estimate the population sizes in their cultures three times per week. The cultures are cleaned weekly by centrifugation and replacement of about half the medium with fresh medium.

Students plot population size versus time for each culture on a daily basis. When the population has filled the container - or when population size has leveled off - students use nonlinear regression to evaluate their data against exponential and logistic models of population growth. The analysis is outlined in the accompanying files: one describes the analysis in SPSS and the other provides an Excel template for graphing both the data and the calculated nonlinear regressions. These files also describe the calculations necessary to estimate the competition coefficients and predict whether the two species can coexist in the laboratory culture.

Allelopathy

In this experiment, students study the allelopathic effects of commonly used herbs on the germination and early growth of other plant species. The system can serve as a model for examining allelopathy in naturally occurring ecological communities and in introduced plants.

The experimental methods are straightforward. Students prepare aqueous extracts of common herbs (oregano, rosemary, sage, thyme - any aromatic herb would serve), filter the extracts through several layers of cheesecloth, and then test the effects of the extracts on the seeds of other plants (lettuce, radish, rye, wheat - any seed that is expected to germinate within a couple of days).

More specifically, students grind 100-150 g of herb leaves with about 150 ml of spring water in a blender. After filtration through cheese cloth, a fixed quantity of extract is applied to a layer of filter paper in a large petri dish (~15 cm in diameter). A fixed number of test seeds (25 or more seeds of one species) are then spread evenly on the filter paper; another layer of filter paper is placed on top of them; and a fixed quantity of the herb extract is applied to the top filter paper. Plain spring water is used instead of an herb extract in the control treatment. The petri dishes are then stacked, wrapped tightly with plastic wrap and then stored in a dark cupboard at room temperature for about five days. The stacks of test plates can be transferred to a refrigerator to inhibit further growth of the seedlings.

In lab the following week, students unwrap the petri plates, score how many seeds have germinated, and then measure the length of the young shoots and roots (to 0.1mm) of germinated seeds with an electronic calipers.

Once the data are collected, students use the accompanying files to conduct a chi-square test to detect differences in germination frequency and ANOVA to test for differences in root and shoot length among treatments. The instructions for running ANOVA should be run first because it includes the directions for formatting the data.

Because all members of the class pool their data, this experiment generates a large and varied data set. Student analyses and reports usually focus on either the effects of different herbs on one species of seed or the effects of one herb on several species of seeds.